{
  "abstract": "This paper shows that an almost-isometric Sobolev map from a Lipschitz subset of an oriented manifold $M$ into another oriented manifold $N$ can be approximated by a map of class $C^{1,α}$, with a universal bound on the $W^{2,m}$ norm, for any $m\\in(1,\\infty)$. This, in turn, implies a universal bound on the $C^{1,α}$ seminorm. The $W^{1,p}$ distance of the approximation from the original map is controlled in terms of the $L^p$-deviation from being an isometry, with the optimal scaling. The manifolds $M$ and $N$ are assumed to be compact, oriented and have equal dimension; $M$ may have a boundary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37249",
  "author_total": 3,
  "authors": [
    {
      "name": "Sergio Conti"
    },
    {
      "name": "Georg Dolzmann"
    },
    {
      "name": "Stefan Müller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ez6mnw7mfh2y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37249",
  "fulltext_url": null,
  "id": "7ez6mnw7mfh2y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37249",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.37249",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ez6mnw7mfh2y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37249",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37249"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uniform $W^{2,m}$ approximation of almost isometric maps",
  "title_text": "Uniform W^2,m approximation of almost isometric maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/7ez6mnw7mfh2y",
  "venue": "arXiv",
  "versions": []
}